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Proof step 101 from proof inv-renam (previous step)

dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), err = ESUCCESS, ino0 = ROOT_INO, entries0[str] ≠ ROOT_INO, p ≠ ε, dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), pw(user, dirs[entries0[str]].meta), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, ¬ q + str ' ⊑ p, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪vfs_walk#(parent(p), user, dirs, files, asynced; ino0, err); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); if err = ESUCCESS then vfs_may_lookup#(ino0, user, dirs, files, asynced; inode, err); p_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err = ESUCCESS then {afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino0, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino0, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 102:
dirs[ino1] = mkdir(m0, md0, # links(ino1, dirs), m3, entries0), dirs[entries0[str]] = mkdir(m, md, m1, m2, entries), err = ESUCCESS, ino0 = ROOT_INO, dom of < ino2, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪vfs_walk#(parent(p), user, dirs, files, asynced; ino0, err); inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); if err = ESUCCESS then vfs_may_lookup#(ino0, user, dirs, files, asynced; inode, err); p_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(p.last); if err = ESUCCESS then {afs_lookup#(ino0, dirs, files, asynced; dent, err); if err = ENOENT then vfs_may_create#(ino0, dent, user, dirs, files, asynced; inode, err) else if err = ESUCCESS then {isdir := true; vfs_may_delete_check#(ino0, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}}; new_inode := inode; new_dent := dent; new_dent_inode := p_inode; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then let dent = new_dent in {old_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md0, true, # links(ino1, dirs), m3, m0) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); old_dent := mkdentry(str, entries0[str]); old_dent_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent, new_dent, err, dirs, files; asynced); if dent.dentry? then vfs_put_inode#(new_dent_inode, of, asynced; err, dirs, files)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), entries0[str] = ROOT_INO, p = ε, q + str ' ⊑ p

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[entries0[str]], m, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[entries0[str]], m, md, m1, m2, entries